Refined error estimates for the Riccati equation with applications to the angular Teukolsky equation

Abstract

We derive refined rigorous error estimates for approximate solutions of
Sturm-Liouville and Riccati equations with real or complex potentials. The approxi-
mate solutions include WKB approximations, Airy and parabolic cylinder functions,
and certain Bessel functions. Our estimates are applied to solutions of the angular
Teukolsky equation with a complex aspherical parameter in a rotating black hole
Kerr geometry.